Field Dependence of Magnetoconductivity

Abstract

A theoretical calculation of the magnetic field dependence of the elements of the conductivity tensor has been performed for a crystal with a general electronic energy band structure. It was assumed that the Boltzmann equation is valid, and that an energy-dependent relaxation time exists. The results are the same as would be given by a superposition of electron gases, whose cyclotron frequencies are related harmonically. The strengths of the harmonics depend upon the energy band structure; in particular, there are certain relations among them which are required by symmetry. The diagonal elements of the conductivity tensor are found to be monotonically decreasing functions of the magnetic field strength. Extension of the calculation to alternating electric fields reveals harmonics in the cyclotron resonance.